Stitz-Zeager_College_Algebra_e-book

# Solving 2 2 we nd x 43 k for integers k two of these

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Unformatted text preview: ssmates. (a) f (x) = cos(3x) + sin(x). Is this function periodic? If so, what is the period? (b) f (x) = sin(x) x. What appears to be the horizontal asymptote of the graph? (c) f (x) = x sin(x). Graph y = ±x on the same set of axes and describe the behavior of f . (d) f (x) = sin 1 x . What’s happening as x → 0? (e) f (x) = x − tan(x). Graph y = x on the same set of axes and describe the behavior of f . (f) f (x) = e−0.1x (cos(2x) + sin(2x)). Graph y = ±e−0.1x on the same set of axes and describe the behavior of f . (g) f (x) = e−0.1x (cos(2x) + 2 sin(x)). Graph y = ±e−0.1x on the same set of axes and describe the behavior of f . 7. Show that a constant function f is periodic by showing that f (x + 117) = f (x) for all real numbers x. Then show that f has no period by showing that you cannot ﬁnd a smallest number p such that f (x + p) = f (x) for all real numbers x. Said another way, show that f (x + p) = f (x) for all real numbers x for ALL values of p > 0, so no smallest value exists to satisfy the deﬁnition of ‘period’. 10.5...
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